The present invention concerns a system and method that allows one to discover how an individual mentally represents a domain described by a series of items. Specifically, the goal is to determine how these items are ordered mentally by asking a certain number of questions in a comparative manner, by taking into account the distance between items, by minimizing the number of questions asked, and by taking into account the inconsistencies in the mental representation of the domain investigated.
When a person orders a series of items on a numerical scale through a series of answered questions, the answers given may be inconsistent or unstable. In other words, the relation given between items A and B, between B and C, and by A and C may not be totally transitive. In this light, how is it possible to assure that the final order of the N items is as consistent as possible with the representation system for the items done by the individual, in a minimum amount of questions, and by taking into account the distance between the items ? This is the problem addressed by the system and method of investigation and of analysis called QualiaSort.
In the social sciences and particularly within psychology, there exists many ways to ask questions on a given topic. For one, an individual can freely and verbally answer open questions on a given topic. Secondly, closed questions can be presented where there are a given number of possible answers. These questions can involve yes/no answers, multiple nominal choices (several possible answers without any order amongst them), ordinal choices (an existing grade amongst these choices), and choices on a numerical scale.
In the last case, the goal of statistic questioning is often to construct a scale on a specific dimension relevant to the circumscribed domain. Subsequently, this scale will permit to position an individual relative to others in the same age group, sex group, social class group, etc.
Equally useful could be the construction of a given order amongst these items. We can consider for instance, marketing surveys seeking to know the preferences of consumers for certain brands of detergents or cars.
Several method of asking questions have been developed over the years in the domain of social sciences in order to classify a list of items in an increasing sequence. For example, the task of an individual can be to directly order a list of N items in an increasing, by assigning each item a number between 1 and N, without any items having the same rank. This method is advantageous since the procedure is easy to understand by the participants and the answers given are clear-cut. The major inconvenience is the absence of information on the distance between items; two successive items can be very distant while they follow one another in the sequence. Another limiting aspect is the fact that items can be ordered in function of importance while they may not be important at all to the participant. Last but not the least, individuals have difficulty handling a large number (roughly more than 7) of items simultaneously when attempting to make out a global idea of a list of items. In conclusion, this method of asking questions suffers from sever limitations, without mentioning the weak performance from the statistical techniques used for analysing ordinal type data such as in the present case.
Another method simply consists of assigning a value or intensity to the preference of each item such as on a scale from 1 to 10, for example. The main advantage is the speed and easiness in which the data can be manipulated. The disadvantage is that the values assigned are not easy to compare from one individual to the next. Is the internal scale adopted by each equivalent, that is, is a 3 and a 7 on a scale from 1 to 10 represent the same intensity for all participants ? We can doubt of this.
Another inconvenient concerns the xe2x80x9cnaturalxe2x80x9d aspect of the measure. When an individual questions his preference between two competing brands, how will he solve the problem? Will he assign a score to each brand and then keep the one with the highest score? Or will he simply ask himself which one he prefers? The one on the left or the right? Will I eat a steak or pizza? Will I go to the movies or rent a video? It seems more natural to compare two items at a time and choose the item that has the highest intensity for the xe2x80x9cvariablexe2x80x9d or dimension examined.
Interrogation methods by comparisons are not recent. They usually serve, as mentioned earlier, to construct a score on one dimension. The fact of conducting several comparisons of elements from similar categories makes it possible to establish the preference for a particular category.
For example, the Myer-Briggs test establishes a global profile on several dimensions (perception vs. sensation, intuitive vs. analytical, etc) by proposing several pairs of expressions that polarizes one or the other of the dimensions.
When the problem concerns the comparison of items with the goal of establishing their sequence in an increasing order, especially when the number of items is significant, it is important to find an appropriate method of asking questions that takes into account the cognitive limits of individuals.
These cognitive limitations are crucial since it dictates how the method of asking questions should be structured. The most important of these limitations is the fact that individual representations of a particular domain are not necessarily coherent or mathematically transitive. If someone evaluates their level of preference, or the intensity of their desire, or any other measure commonly referred to as a mathematical or statistical xe2x80x9cdistancexe2x80x9d between two items A and B by a value d[A,B], and that between B and C as d[B,C], then the measure between A and C will not necessarily be equivalent to the sum of d[A,B] and d[B,C].
The absence of coherence between the representations is the source of many difficulties in terms of investigation. If all of the relations would be perfectly transitive, then in order to determine the distance between each item, it would suffice to compare items that are neighbours (xi and xi+1 for all i between 1 and N). In order to determine the distance, say between item 7 and item 25, it would be sufficient to add the distance between each item separating these items (d[7,8]+d[8,9]+d[9,10]+ . . . +d[24,25]). The result would be precise while adopting the most synthetic evaluation procedure. Unfortunately, since these relations are not purely transitive, the procedure must be improved to take this limitation into account.
Another major limitation is tied to the cognitive overload involved in each method of asking questions. The individuals having to respond to a questionnaire, be it in on paper or on electronic form, cannot stay concentrated on a similar task for a long period of time. Hence, it is desirable to limit the number of questions to reduce the risk of fatigue or stress, which would probably reduce the reliability of the answers provided. If this limitation would not exist, researchers could permit themselves the luxury of asking hundreds of questions without any concerns for the performance of the participants.
An object of the invention is an investigative and analytical method based on comparisons of pairs. The goal is to order a relatively long list of items while taking into account the absence of perfect coherence in the individual""s representations as well as restricting the number of questions. Such a system can be used for example, for marketing surveys on individual""s preferences for different brands of cars, in industrial psychology for measuring an individual""s abilities relative to a series of activities done in a professional context, in clinical psychology for measuring all auto-perceptions for a particular domain, or in various investigations where we want to rapidly determine the opinion (universe of representations) of individuals on a particular topic.
In accordance with the invention, this object is achieved with a method for inferring mental representations by successive comparison of items, comprising the steps of:
(a) presenting a series of N items to a participant;
(b) asking the participant to compare each pair of items, where each item is compared with its immediate neighbour, except for the items at the two extremes which are compared to one another, so that each item is used in a pair twice, and N comparisons are done;
(c) ordering the items by matrix iteration in order to obtain a new sequence of items;
(d) elaborating a new list of N/2 paired items, on the basis of immediate neighbours, taking each item only once;
(e) asking the participant to compare each pair of items elaborated in step (d);
(f) integrating the responses of steps (a) to (e) into a matrix; and
(g) finally ordering the items based on the matrix obtained in step (f).